Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Quanwu Mu"'
Publikováno v:
Journal of Mathematics, Vol 2021 (2021)
Let k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real numbers, not all of them have the same sign, and λ1/λ2 is irrational. It is proved that the inequality λ1p1+λ2p22+λ3p33+λ4p44+λ5p5k+η
Externí odkaz:
https://doaj.org/article/06416718d1bb4cc4b3cc19e43dce5d56
Autor:
Quanwu Mu, Zhipeng Gao
Publikováno v:
The Ramanujan Journal. 60:551-570
Publikováno v:
Czechoslovak Mathematical Journal. 69:353-363
Let k ⩾ 5 be an odd integer and η be any given real number. We prove that if λ1, λ2, λ3, λ4, μ are nonzero real numbers, not all of the same sign, and λ1/λ2 is irrational, then for any real number σ with 0 < σ < 1/(8ϑ(k)), the inequality
Publikováno v:
International Journal of Number Theory. 14:1651-1668
It is proved that if [Formula: see text] are nonzero real numbers, not all of the same sign and [Formula: see text] is irrational, then for given real numbers [Formula: see text] and [Formula: see text], [Formula: see text], the inequality [Formula:
Autor:
Quanwu Mu
Publikováno v:
Frontiers of Mathematics in China. 12:1457-1468
Let d ≥ 3 be an integer, and set r = 2d-1 + 1 for 3 ≤ d ≤ 4; r = 17/32∙d+1 for 5 ≤ d ≤ 6; r = d2+d+1 for 7 ≤ d ≤ 8; and r = d2+d+2 for d ≥ 9; respectively. Suppose that Фi(x, y) ∈ Z[x, y] (1 ≤ i ≤ r) are homogeneous and nonde
Autor:
Quanwu Mu
Publikováno v:
International Journal of Number Theory. 13:1531-1545
Let [Formula: see text] be an integer with [Formula: see text] and [Formula: see text] be any real number. Suppose that [Formula: see text] are nonzero real numbers, not all of the same sign and [Formula: see text] is irrational. It is proved that th
Autor:
Xiaodong Lü, Quanwu Mu
Publikováno v:
Journal de Théorie des Nombres de Bordeaux. 28:523-538
Autor:
Quanwu Mu
Publikováno v:
The Ramanujan Journal. 39:481-496
Let k be an integer with \(k\ge 3\) and \(\eta \) be any real number. Suppose that \(\lambda _1, \lambda _2, \lambda _3, \lambda _4, \mu \) are non-zero real numbers, not all of the same sign and \(\lambda _1/\lambda _2\) is irrational. It is proved
Publikováno v:
International Journal of Number Theory. 11:2065-2072
This paper is concerned with the metric properties of the generalized continued fractions (GCFϵ) with the parameter function ϵ(kn), where kn is the nth partial quotient of the GCFϵ expansion. When -1 < ϵ(kn) ≤ 1, Zhong [Metrical properties for
Autor:
Quanwu Mu
Publikováno v:
Journal of Number Theory. 145:109-125
Let P r denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that for each integer k with 4 ≤ k ≤ 5 , and for every sufficiently large even integer N satisfying the congruence conditi